There is a connection between nonlinear partial differential equations that can be solved by the inverse scattering transform and nonlinear ordinary differential equations without movable critical points (e.g., Painlevé transcendents). We exploit this connection to reduce the second equation of Painlevé to a linear integral equation. We also describe a class of nonlinear ordinary differential equations that can be exactly linearized by this method.

• Received 17 February 1977

DOI:https://doi.org/10.1103/PhysRevLett.38.1103